Abstract The phenomenon of bifurcation in disease transmission models has been observed in a number of epidemiological models. The consequence of bifurcation is that the classical requirement of the reproduction number being less than unity becomes only a necessary. but not sufficient. for disease elimination. https://www.roneverhart.com/2-1-2-x-1-4-x-36-Smooth-Saddle-Threshold-NGP-410-36/